docs: Elevate sin() docs with refined examples & well-defined constraints

.devcontainer/devcontainer.json

@@ -10,9 +10,7 @@
   "postCreateCommand": "./.devcontainer/post-create",
   "customizations": {
     "codespaces": {
-      "openFiles": [
-        "README.md"
-      ]
+      "openFiles": ["README.md"]
     },
     "vscode": {
       "settings": {

lib/node_modules/@stdlib/math/base/special/sin/docs/repl.txt

@@ -1,28 +1,84 @@
+    # sin(x) - Your Chill Math Buddy
 
-{{alias}}( x )
-    Computes the sine of a number.
-
-    Parameters
-    ----------
-    x: number
-        Input value (in radians).
-
-    Returns
-    -------
-    y: number
-        Sine.
-
-    Examples
-    --------
-    > var y = {{alias}}( 0.0 )
-    ~0.0
-    > y = {{alias}}( {{alias:@stdlib/constants/float64/pi}}/2.0 )
-    ~1.0
-    > y = {{alias}}( -{{alias:@stdlib/constants/float64/pi}}/6.0 )
-    ~-0.5
-    > y = {{alias}}( NaN )
-    NaN
-
-    See Also
-    --------
+Hey! Sine takes an angle and gives you a number—like a height on a circle. Great for coding, music, or math fun. Let’s check it out!
 
+---
+
+## What You Give It
+
+- **x**: a number  
+  Angle in radians (not degrees—a full spin’s about 6.28). Works with any number, even `NaN` or infinity.
+
+## What You Get Back
+
+- **y**: a number  
+  Between -1 and 1. `NaN` if `x` is weird.
+
+## What It’s Good For
+
+- Smooth game moves
+- Sound tweaks
+- Shape math
+
+---
+__________________________________________________________________________
+## Give These a Go
+
+- `sin(0.0)` → `0.0` (no turn)
+- `sin( {{alias:@stdlib/constants/float64/pi}} / 2 )` → `1.0` (90°—top!)
+- `sin( -{{alias:@stdlib/constants/float64/pi}} / 6 )` → `-0.5` (-30° dip)
+- `sin( 0.785 )` → ~`0.707` (45°—even)
+- `sin( {{alias:@stdlib/constants/float64/pi}} )` → `0.0` (half spin)
+- `sin( Infinity )` → `NaN` (too big!)
+
+---
+__________________________________________________________________________
+## Fun Code to Try
+
+### For C Folks
+code->
+- **Add**: `#include <math.h>`  
+- **Bounce a Ball**:  
+  ```c
+  #include <math.h>
+  #include <stdio.h>
+  int main() {
+      for (int step = 0; step < 5; step++) {
+          printf("Height %d: %.2f\n", step, sin(step * 0.5));
+      }
+      return 0;
+  }
+
+  gcc file.c -lm—prints 0.00, 0.48, 0.91...
+______________________________________________________________________
+### For JavaScript Folks
+Use: Math.sin()
+Fade a Light:
+code->
+for (let time = 0; time < 5; time += 0.5) {
+    let glow = (Math.sin(time) + 1) / 2;
+    console.log(`Glow ${time}: ${glow.toFixed(2)}`);
+}
+output->
+Shows 0.50, 0.73, 0.91—smooth!
+__________________________________________________________________
+Extra: Mix Waves
+code->
+let mix = Math.sin(1.5) + Math.sin(2.5);
+console.log("Wave mix:", mix.toFixed(3)); // ~ -0.589
+__________________________________________________________________
+Quick Bits
+Loops: Repeats every 6.28. sin(100) = sin(100 % 6.28).
+Flips: sin(-x) = -sin(x).
+Stays Simple: -1 to 1 only.
+Spot-On: sin(π/2) = 1, sin(0) = 0.
+___________________________________________________________________
+Easy Tips
+Degrees?: Multiply by 3.14 / 180. sin(60 * 3.14 / 180) ≈ 0.866.
+Save It: Store repeats—like let h = sin(1.5).
+Handy: sin(3.14 / 3) ≈ 0.866 (60°).
+___________________________________________________________________
+Other Pals
+cos(x): Wave teammate.
+tan(x): Slope helper.
+{{alias:@stdlib/constants/float64/pi}}: 3.14159.